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By John Stuart Mill

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Additional info for A System of Logic Ratiocinative and Inductive, Part I (The Collected Works of John Stuart Mill - Volume 07)

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XXX INTRODUCTION and must be thrown into it when assurance of scientific accuracy is needed and desired" (203). The task of determining whether Socrates or the Duke of Wellington have the marks which justify bringing them under the general formula, All men are mortal, is easily accomplished by observation, and the result stated in the minor premise. But not all cases are so simple. The minor premise may by itself have to be established by an induction followed by a deduction or interpretation, that is, by a syllogism.

Geometry rests on a very few simple inductions, the formulae of which are expressed in the axioms and a few of the so-called definitions. The remainder of the science is made up of the processes employed for bringing unforeseen eases within these inductions; or (in syllogistic language) for proving the minors necessary to complete the syllogisms; the majors being the definitions and axioms. In those definitions and axioms are laid down the whole of the marks, by an artful combination of which it has been found possible to discover and prove all that is proved in geometry.

W]hatever can be eliminated, is not connected with the phenomenon by any law .... ) To return now to the definition of logic as the science as well as the art of reasoning, in which the science consists of an analysis of the mental process which takes place when we reason, and the art consists of the rules grounded on that science, it can be said that in the case of induction the mental process consists in the solving of a problem stated in its full generality. Mill discovers what this mental process is by directly solving the problem himself.

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